A known class of DSP filters operate by successively sampling the input signal and implementing the following discrete Fourier approximation:
      R    =                                                      S              s                        ·                          S              s                                +                                    S              c                        ·                          S              c                                          ⁢                          ⁢      where                          S        s            =                        ∑                      n            =            0                    m                ⁢                                  ⁢                              X            n                    ·                      sin            ⁡                          (                              f                ·                k                ·                n                            )                                            ,                  S        c            =                        ∑                      n            =            0                    m                ⁢                                  ⁢                              X            n                    ·                      cos            ⁡                          (                              f                ·                k                ·                n                            )                                          
One such type of filter is known as a Finite Impulse Response (FIR) filter. The input signal is sampled, and each sample is fed in turn to a series of multipliers the other input to which is one of the Fourier coefficients or its analog. As one sample is shifted out of a first multiplier to the next one, the next sample in time is presented to the first multiplier, and so on.
While the foregoing approaches have proven useful for lower frequencies requiring moderate sampling rates, they remain impractical for frequencies approaching 1 Ghz. This is due principally to the number of analog to digital conversions and calculations required at high sampling rates and to limitations in the processing speed of the digital components involved.
It is an object of the present invention to provide a means for identifying or extracting a signal using a discrete approximation analysis, but that is suitable for frequencies well in excess of 1 Ghz.